Resolution of high order WENO schemes for complicated flow structures

In this short note we address the issue of numerical resolution and efficiency of high order weighted essentially nonoscillatory (WENO) schemes for computing solutions containing both discontinuities and complex solution features, through two representative numerical examples: the double Mach reflection problem and the Rayleigh-Taylor instability problem. We conclude that for such solutions with both discontinuities and complex solution features, it is more economical in CPU time to use higher order WENO schemes to obtain comparable numerical resolution.

[1]  David H. Sharp,et al.  The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces , 1987 .

[2]  Chi-Wang Shu,et al.  The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V , 1998 .

[3]  R. Rosner,et al.  On the miscible Rayleigh–Taylor instability: two and three dimensions , 2001, Journal of Fluid Mechanics.

[4]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[5]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[6]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[7]  Ravi Samtaney,et al.  On initial‐value and self‐similar solutions of the compressible Euler equations , 1996 .

[8]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[9]  C. Angelopoulos.  High resolution schemes for hyperbolic conservation laws , 1992 .

[10]  Jean-François Remacle,et al.  An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems , 2003, SIAM Rev..

[11]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[12]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[13]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[14]  Centro internazionale matematico estivo. Session,et al.  Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , 1998 .